This project aims to develop new models for randomness in the size of a human population which explicitly recognize different levels at which random influences impinge and to apply these new models to an understanding of the long-term processes which regulate population size and growth and counteract cumulating randomness. The new models will combine and refine existing statistical models for "demographic" and "environmental" randomness. Long-term data are required to estimate parameters in stochastic homeostatic models. For this project, the long series of parish demographic counts for England before 1811 of Wrigley and Schofield (1981) will provide a data set for estimating parameters of the model and studying patterns of covariation of demographic rates. The models will then be applied to the problem of evaluating the strength of homeostatic tendencies required to have maintained low average growth over human prehistory, and to a comparison of existing theories of human population regulation with new theories of "liberal population regulation" in biology. The project should provide a better basis for understanding the long-term dynamics of limited population growth.